An organic light-emitting diode display may contain an array of display pixels. Each display pixel may have a respective organic light-emitting diode that is controlled by a drive transistor. At low temperatures, it may be necessary to increase the amount of current through an organic light-emitting diode to achieve a desired luminance level. In order to increase the current through the light-emitting diode, the ground voltage level may be lowered. However, this may lead to thin-film transistors within the pixel leaking, which may result in undesirable display artifacts such as bright dots being displayed in a dark image. In order to prevent leakage in the transistors, the transistors may be coupled to separate reference voltage supplies or separate control lines. Additionally, the transistors may be positioned to minimize leakage even at low ground voltage levels.